Heterograft copolymers of poly(ε‐caprolactone) prepared by combination of ATRA “grafting onto” and ATRP “grafting from” processes

This paper aims at reporting on the synthesis of a heterograft copolymer by combining the “grafting onto” process based on atom transfer radical addition (ATRA) and the “grafting from” process by atom transfer radical polymerization (ATRP). The statistical copolymerization of ε‐caprolactone (εCL) and α‐chloro‐ε‐caprolactone (αClεCL) was initiated by 2,2‐dibutyl‐2‐stanna‐1,3‐dioxepane (DSDOP), followed by ATRA of parts of the chlorinated units of poly(αClεCL‐co‐εCL) on the terminal double bond of α‐MeO,ω‐CH₂?CH? CH₂? CO₂‐poly(ethylene oxide) (PEO). The amphiphilic poly(εCL‐g‐EO) graft copolymer collected at this stage forms micelles as supported by dynamic light scattering (DLS) and transmission electron microscopy (TEM). The unreacted pendant chloro groups of poly(εCL‐g‐EO) were used to initiate the ATRP of styrene with formation of copolymer with two populations of randomly distributed grafts, that is PEO and polystyrene. © 2006 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 44: 6015–6024, 2006     

Etude de la réaction de l'acétylacétone avec les diamines hétéroaromatiques

The inluence of the starting o-diamine on the reaction products is shown in the condensation of heteroaromatic o-diamines with acetylacetone; 2,3- and 3,4-diaminopyridines gave only a crotonic intermediate providing imidazopyridines. On the other hand, 1,5-diaminoimidazoles gave tow types of compounds, imidazotriazepines and imidazopyridines. Triazolopyridazines were formed from 3,4-diaminotriazoles.     

Nonlinear mean field Fokker-Planck equations. Application to the chemotaxis of biological populations

We study a general class of nonlinear mean field Fokker-Planck equations in relation with an effective generalized thermodynamical (E.G.T.) formalism. We show that these equations describe several physical systems such as: chemotaxis of bacterial populations, Bose-Einstein condensation in the canonical ensemble, porous media, generalized Cahn-Hilliard equations, Kuramoto model, BMF model, Burgers equation, Smoluchowski-Poisson system for self-gravitating Brownian particles, Debye-Hückel theory of electrolytes, two-dimensional turbulence... In particular, we show that nonlinear mean field Fokker-Planck equations can provide generalized Keller-Segel models for the chemotaxis of biological populations. As an example, we introduce a new model of chemotaxis incorporating both effects of anomalous diffusion and exclusion principle (volume filling). Therefore, the notion of generalized thermodynamics can have applications for concrete physical systems. We also consider nonlinear mean field Fokker-Planck equations in phase space and show the passage from the generalized Kramers equation to the generalized Smoluchowski equation in a strong friction limit. Our formalism is simple and illustrated by several explicit examples corresponding to Boltzmann, Tsallis, Fermi-Dirac and Bose-Einstein entropies among others.     

Quasilinear theory of the 2D euler equation

We develop a quasilinear theory of the 2D Euler equation and derive an integrodifferential equation for the evolution of the coarse-grained vorticity omega;(r,t). This equation respects all of the invariance properties of the Euler equation and conserves angular momentum in a circular domain and linear impulse in a channel. We show under which hypothesis we can derive an H theorem for the Fermi-Dirac entropy and make the connection with statistical theories of 2D turbulence.